I didn't just one day decide to apply to a Master's and got it. It was a long process. Let's see some of my journey before even applying to a Master's
During undergrad
Get good grades
It goes without saying, but good grades look really good in an application, but beyond that, ideally, they reflect that you learnt something during your undergrad, in the worst case, they reflect that you learnt to play the game of passing exams, but don't worry! Knowing how to play that kind of game will be helpful when navigating bureaucracy in the future!
Of course, unless they're truly astonishing, it is not enough to only have good grades. If you can show you can also do something, you'll have a better positioning than other students. I wish I had known this in the past.
In my case, I was lucky that in professional Mathematics, the courses and exams in my university where made so that, if you passed them, it had to be because you at least learnt something.
Get undergraduate experience
You have to show you did something other than read books and pass exams.
Research can give you good experience during your undergraduate, this can also be activism or volunteering.
In my case, I had a research project on Control Theory during my undergrad for some months. Don't be impressed, it was mainly about pointing out how there was a mistake in a proof by a not-that-well-known author.
Find out which areas you like
Don't go in "automatic mode" passing courses, eventually, in your major, you'll find some things that pull your interest more than others, and that's ok, it's ok not to be a universal genius (sorry Leibniz, you put too much pressure on us mathematicians!).
In my case, I first studied Physics for some semesters before realizing that Mathematics was my thing, and even inside Math, I enjoyed far more algebra and logic than analysis (sorry again Lebiniz!).
After undergraduate
(me my first unemployed months after finishing my bachelor's)
Work experience
This is when things get tricky.
Ideally, your work will have something to do with the areas you got interested in during undergrad, or with the areas you intend to go to for your Master's.
Not everyone has the luck to have both, or even one.
In my case, my fist job did not start with either option.
As I have detailed before, I started worked in Wolfram Research in a more Computer Science oriented project. Luckily, after a year or so, I could move into another project, more related with linguistics (and at this time I already had decided what Master's to apply to, but that will be for another post)
I speculate that that helped me in my application process: There was concrete proof that someone trusted me with a project with an objective, deadlines, client requirements, etc, and that I did it (to the best of my ability).
Live
It was when my life did not revolve around my studies that I could better discern what I wanted to do with it.
Among scientists there's a bad custom of thinking your studies are your life (and internally your self-worth). This effectively destroys life-work/study balance, and is a recipe for missing on enormous amount of stuff.
Very curiously, it was while I was doing other hobbies that my mind was free of stress. And I say "very curiously" because my past self would devote everything to trying too hard to be too perfectionistic.
I then realized, I did not want to follow the predetermined route for mathematicians and scientists in general:
undergrad > master > doctorate > N post-docs > tenure maybe
">" means " then immediately"
Nah, I wanted to do other stuff as well, not go into academia directly, and now I don't think I even want to go into it at all in the medium term.
Don't be too hard on yourself, follow a path not because it is the default, but because you chose to take it with the consequences it may have :)
So, hear my words:
Quiêscere necesse est = to leisure is a necessity
(chorus: I'm a madman, that realized that time is too short)
Deciding I wanted to do a Master's degree
After my education I had a general base/idea of what different areas of Mathematics do.
But I felt like doing more than just the pure math I had been taught.
I felt like math should not be everything that I do, that I wanted to develop my other interests as well.
That meant I needed more training, so it was that I decided to do a Master's degree: in order to combine what I interested me with something math-related, and why not?, maybe get a better pay-grade with that.
Before this I thought about doing a Master's because "it's what everyone here does", but now I had good personal reasons for doing it.
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